Stemming from centrally planned church architecture, the domestic rotunda type counts as one of the most renowned examples of Renaissance architectural conception. Often considered a physical and earthly manifestation of the divine, architects ordained rotunda symbolism through architectural ratio and proportion. While mostly linked to Italian examples, the rotunda typology also affected British architecture, as derived from the models of Serlio and Palladio. By combining 3D scanning and CAD analyses with historical methods, we scrutinise how commonplace architectural ratios shaped British rotunda plans in the cases of Hopetoun House and Chiswick House. At the same time, the architectural ratio proved a flexible tool to imitate and emulate Italian architectural models in its British context, making evident the richness and versatility of architectural models that British architects collated.

Throughout history, diagrammatic drawing formed a modus operandi for generating architectural typologies, creating spatial hierarchies, codifying ratio and proportion while defining the shape grammar of the edifice. Despite the prominence of the diagram in architectural design, no account of designing irregular sites during the Renaissance exists, nor how diagrams partition space. This paper’s computer-aided graphical analysis elucidates how to design irregular sites by reading principles of partitioning in the treatises of Serlio and Palladio. Through the numeric lexicons of Serlio, Palladio and Bertotti Scamozzi, this paper uncovers the ways the transformative power of the diagram codifies irregular typologies while ordering its spatial hierarchies. The cases of Serlio’s and Palladio’s geometrical reckoning illuminate a commonplace working method for partitioning Renaissance palazzi where the heuristic diagram visually uncovers the architect’s idea by combining context, site, and function that result in architectural inventions.

The facciata double meaning as façade and outer appearance embodies the Italian city-state’s political, cultural, and social values that Leon Battista Alberti outlined in his famed De re aedificatoria libri decem (1485). This concept lies at the heart of Florence’s urban fabric: one of the early cradles of Renaissance architecture that originated from the artistic expenditure of prosperous families including, the Medici, Strozzi, and Rucellai. In this context, the Palazzo Rucellai (c.1446-66) marks an important historical moment in history as its façade, with its three superimposed orders and well-proportioned urban composition, was the first of its kind in Renaissance Florence. However, the palazzo’s unfinished façade sparked a debate regarding its finished appearance which the paper revisits by positioning a 3D digital twin onto the façade’s historic urban context and by applying through Space Syntax to explore its relationship to the urban fabric.

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